DMDA provides a simple way to do domain decomposition of structured grid
meshes in the x, y, and z direction, that is it makes it easy to efficiently
chop up vectors in all 3 dimensions, allowing very large problems easily.
Unfortunately it only goes up to 3 dimensions and attempts to produce versions
for higher dimensions have failed.
If you would like to do domain decomposition across all six of your
dimensions (which I think you really need to do to solve large problems) we
don't have a tool that helps with doing the domain decomposition. To make
matters more complicated, likely the 3d mpi-fftw that need to be applied
require rejiggering the data across the nodes to get it into a form where the
ffts can be applied efficiently.
I don't think there is necessarily anything theoretically difficult about
managing the six dimensional domain decomposition I just don't know of any open
source software out there that helps to do this. Maybe some PETSc users are
aware of such software and can chime in.
Aside from these two issues :-) PETSc would be useful for you since you
could use our time integrators and nonlinear solvers. Pulling out subvectors to
process on can be done with with either VecScatter or VecStrideScatter,
VecStrideGather etc depending on the layout of the unknowns, i.e. how the
domain decomposition is done.
I wish I had better answers for managing the 6d domain decomposition
Barry
> On Jul 29, 2017, at 5:06 PM, Oleksandr Koshkarov <[email protected]> wrote:
>
> Dear All,
>
> I am a new PETSc user and I am still in the middle of the manual (I have
> finally settled to choose PETSc as my main numerical library) so I am sorry
> beforehand if my questions would be naive.
>
> I am trying to solve 6+1 dimensional Vlasov equation with spectral methods.
> More precisely, I will try to solve half-discretized equations of the form
> (approximate form) with pseudospectral Fourier method:
>
> (Equations are in latex format, the nice website to see them is
> https://www.codecogs.com/latex/eqneditor.php)
>
> \frac{dC_{m,m,p}}{dt} =\\
> \partial_x \left ( a_n C_{n+1,m,p} +b_n C_{n,m,p} +c_n C_{n-1,m,p} \right ) \\
> + \partial_y \left ( a_m C_{n,m+1,p} +b_m C_{n,m,p} +c_m C_{n,m-1,p} \right
> ) \\
> + \partial_z \left ( a_p C_{n,m,p+1} +b_p C_{n,m,p} +c_p C_{n,m,p-1} \right
> ) \\
> + d_n E_x C_{n-1,m,p} + d_m E_x C_{n,m-1,p} + d_p E_x C_{n,m,p-1} \\
> + B_x (e_{m,p} C_{n,m-1,p-1} + f_{m,p}C_{n,m-1,p+1} + \dots) + B_y (\dots) +
> B_z (\dots)
>
>
> where a,b,c,d,e,f are some constants which can depend on n,m,p,
>
> n,m,p = 0...N,
>
> C_{n,m,p} = C_{n,m,p}(x,y,z),
>
> E_x = E_x(x,y,z), (same for E_y,B_x,...)
>
> and fields are described with equation of the sort (linear pdes with source
> terms dependent on C):
>
> \frac{dE_x}{dt} = \partial_y B_z - \partial_z B_x + (AC_{1,0,0} + BC_{0,0,0})
> \\
> \frac{dB_x}{dt} = -\partial_y E_z + \partial_z E_x
>
> with A,B being some constants.
>
> I will need fully implicit CrankâNicolson method, so my plan is to use SNES
> or TS where
>
> I will use one MPI PETSc vector which describes the state of the system (all,
> C, E, B), then I can evolve linear part with just matrix multiplication.
>
> The first question is, should I use something like DMDA? if so, it is only
> 3dimensional but I need 6 dimensional vectots? Will it be faster then matrix
> multiplication?
>
> Then to do nonlinear part I will need 3d mpi-fftw to compute convolutions.
> The problem is, how do I extract subvectors from full big vector state? (what
> is the best approach?)
>
> If you have some other suggestions, please feel free to share
>
> Thanks and best regards,
>
> Oleksandr Koshkarov.
>
